Question: How many natural numbers between 150 and 300 are divisible by 9?
Solution: For a number to be divisible by $9$, the sum of its digits must also be divisible by $9$. Thus, the least and greatest numbers in the range from $150$ to $300$ that are divisible by nine are $153$ and $297$.  So, we must count the numbers in the list  \[9\cdot 17, 9\cdot 18, 9\cdot 19, \ldots, 9\cdot 33.\] This list has the same number of numbers as the list \[17, 18, 19,\ldots, 33.\] Subtracting 16 from each of these gives  \[1,2,3,\ldots,17.\] There are clearly $\boxed{17}$ numbers in this list.